Homology (mathematics) Main article:Homology theory Simplex Simplicial complex Polytope Triangulation Chain (mathematics) Betti number Euler characteristic Genus Singular homology Mayer-Vietoris sequence Applications Jordan curve theorem Brouwer fixed point theorem Invariance of domain Borsuk-Ulam Theorem Homotopy theory Homotopy Fundamental group Seifert-van Kampen theorem Winding number Simply connected Universal cover Monodromy Fibre bundle Möbius strip Line bundle Vector bundle Associated bundle Fibration Further developments Künneth theorem De Rham cohomology Characteristic class Chern class Chern-Simons form Pontryagin class Poincaré conjecture K-theory Cobordism Hodge conjecture Weil conjectures Homological algebra Chain complex Commutative diagram Exact sequence Five lemma Short five lemma Snake lemma Splitting lemma Extension problem Abelian category Group cohomology Sheaf Grothendieck topology History Combinatorial topology
